The Voyager spacecraft are on solar escape trajectories into the interstellar medium. Each Voyager carries a phonograph record encoded with depictions of life and culture on Earth, intended as a ‘message in a bottle’ to distant epochs. Due to the benign environment of interstellar space the records may be preserved after other cultural/technological artifacts are erased from the Earth’s surface. It is thus of anthropological interest to investigate the trajectory and fate of the spacecraft that may carry some of the final evidence of human civilization. We evaluate the eventual degradation of the records from interaction with interstellar matter. We find that after traveling for 5 Gyr in a smooth axisymmetric galactic potential, Voyager 1 is ~99% likely to suffer damage rendering the exterior-facing side of the record indecipherable, while Voyager 2 is only ~20% likely to suffer similar damage. We find that the spacecraft-facing side of both records will likely survive until the merger of the Milky Way and M31 in ~5 Gyr, after which it becomes possible that the spacecraft are ejected into the intergalactic medium and erosion rates reduce accordingly.